Which has the higher statistical expected value: Playing the slots or the roulette wheel in Las Vegas (let’s skip card games where there is any element of skill whatsoever), or the typical state-sponsored lottery?
I know that they’re both negative, but I’m wondering if one has an edge for the player.
IIRC the standard roulette wheel (2 green numbers) has a built in 5.25% advantage for the house (called the vig). If you play odd-even, black-red you have an almost 50-50 chance of winning. You basically have no chance of winning the lottery. Of course the level of risk is much higher. In the lottery you only have to put out a dollar. In Vegas if you want to win big you have to bet big.
In either case the house always wins in the end.
An odd-even, black-red roulette bet is even money, paying one dollar on a one dollar bet. The odds of winning your dollar back in the Powerball is a little harder to compare, because the smallest payout is $3, or odds of 1:68.96, so if you divide by three, the odds of doubling your money is 1:22.98. Not as good as roulette, but better than no chance.
For state lotteries, the expected return can be positive, if the jackpot is big enough.
For example, in the multi-state “Mega Millions”, a $1 ticket has a 1 in 176 million chance of winning the jackpot. If that jackpot is worth more than $176M, the expected return of a ticket is positive. Of course, the chance of winning is still extremely small. And I’m ignoring the effects of non-jackpot prizes and multiple winning tickets.
Not for virtually all casinos in the U.S. They want their cut and get it on those bets on the “0” and “00”. Those are both losers on the two bets you listed making the odds not nearly as good.
As pointed out above, because lottery pots grow when the game was not won last time, the payout can be positive. There were (are) groups of people who would play every number to hopefully make a profit. This method can backfire if there are multiple winners, as the pot is divided.
Huh? There is nothing wrong with what he said. An even-money bet is a bet that pays 1:1. The odd/even bets pay 1:1, so it is an even-money bet. So is blackjack (most of the time), pass/don’t pass in craps, and a few other games that either don’t use paytables or don’t use a paytable on, say, the ante. Just because the odds of getting even or odd aren’t 1:1 on a single-zero or double-zero wheel doesn’t mean the bet isn’t even-money.
Right. I’ve always suspected that the number of tickets sold grows faster than the jackpot after a certain point. The highest expected value might be at a high mid range (not record) jackpot.
At least you have a positive expected value sometimes in power ball, something you never have in roulette.
Powerball is a better game than roulette on an EV basis.
I was talking more about expected return which I think is way more relevant to the thread topic but I suppose that the terminology does mean that the original statement was stated correctly.
Putting aside the rather substantial distorting effect of rollover jackpots (already discussed), my understanding is that the default model (lets say for week zero, after the jackpot was won the previous week) is that the state rakes off half of the ticket sales and the prize pool is the other half.
That’s horrible odds, worse than Keno, worse than the Big Wheel. Different slot machines are programmed to be looser or tighter, but I’d doubt many rake off more than 20% (which is still huge). Parimutuel tracks rake off IIRC about 15%.
True. We need to figure what the jackpot has to be to have a 0 EV, assuming no split jackpots. That aspect can be modeled in later if we had jackpot size v. ticket sales data. We could come out with a model that predicts roulette is a better bet under jackpot X, while powerball is a better bet over X.
Another thing to remember when computing the expected payout of a large sum state or multi-state lottery is that the advertised payout is for the simple sum of the payments that an 20 or 25 year annuity will pay the winner. If there is a cash value payment option, it is always substantially smaller.
Furthermore, when you win the lottery (and technically for all gambling winnings exceeding gambling losses), you will have to pay state and federal income tax on your winnings which will reduce the effective return.
I think it can be stated rather simply: the amount rolled over must at least equal the state’s rakeoff on the “second round”. If we assume the rakeoff is always a simple 50%, this would happen if the amount bet was not more than twice the rollover (IOW, it was no more than was bet on the first round). This is surely quite rare, as rollovers create big prizes which reliably enhance betting interest.
Split jackpots are always a possibility, and that assumption isn’t needed for the expected value calculation.
Apart from its enormous impracticality, the scheme of buying one ticket for each possible number is a poor one precisely because of the split-jackpot possibility. If you do this, you are effectively betting that without your participation another rollover would have happened. In the case of a large jackpot and the attendant betting frenzy, that’s not likely.
Absolutely. This is an applied statistics question.
As an example, suppose we have a roulette wheel with 1-36 plus 0 and 00. The payoff may be 1:1 for an odd/even bet (that is, if you bet $1 and win, you keep your $1 and win $1). If the probability of winning were 0.5, then the expected value would be exactly 0. However, the probability of winning is not 0.5, it’s 0.4737. So for each time you bet, 0.4737 times you’d be up a dollar and 0.5263 times you’d be down a dollar. The fact that the payable odds are 1:1 is totally irrelevant, and may even mislead the naive gambler.
The *expected value * is therefore -$0.0526 per $1 bet, as mentioned by Loach.
Although I don’t know the facts, I would think it would be outrageous for a state to skim 50% of lottery revenues.
You may think it outrageous, but it’s not far off:
http://www.louisianalottery.com/index.cfm?md=pagebuilder&tmp=home&navID=78&cpID=28&cfmID=0&catID=0
or
or cf.
http://www.lohud.com/apps/pbcs.dll/article?AID=/20070129/NEWS05/701290338/1021/NEWS05
This isn’t surprising when you recall that lotteries were approved in almost every U.S. state as a putative source of windfall funding for education, and not as a form of gambling (heaven forbid) to compete with other games of chance.